Seminar

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Abstract: Geometric vertex decomposition (a degeneration technique) and liaison are two frameworks that have been used to produce similar results about similar families of algebraic varieties. In this talk, I will describe an explicit connection between these two approaches. In particular, I will show that each geometrically vertex decomposable ideal is linked by a sequence of ascending elementary G-biliaisons of height 1 to an ideal of indeterminates and, conversely, that each elementary G-biliaison of a certain type gives rise to a geometric vertex decomposition. As an application, I will show that several well-known families of ideals are glicci. I will also explain how this connection provides a framework for implementing, with relative ease, Gorla, Migliore, and Nagel's strategy of using liaison to establish Gr\"obner bases.

The first half of the talk will focus on background and motivation, and the second half will be on the above-mentioned work, which is joint with Patricia Klein.

Notes 8.18 MB application/pdf

Geometric Vertex Decomposition And Liaison